sub-Nyquist Sampling Research Articles

Modified low-bandwidth sub-Nyquist sampling receiving scheme in an IM/DD OFDM system enabled by improved optical shaping.

In this paper, a modified low-bandwidth sub-Nyquist sampling receiving scheme enabled by optical shaping is investigated in an intensity modulation/direct detection (IM/DD) orthogonal frequency-division multiplexing (OFDM) system, which can reduce the sampling rate and analog bandwidth of an analog-to-digital converter (ADC) at the receiving end. By changing the phase matrix of preprocessing, the modified scheme can distinguish different groups of data only by controlling the delay of the shaping module. In addition, the proposed RF sharing architecture can further reduce the cost and increase the feasibility of the scheme. Based on arcsine digital pre-distortion (DPD) technology, a DPD optical pulse shaping scheme is proposed to achieve better spectrum aliasing in the optical domain. With the help of the DPD shaping, we successfully experimentally demonstrate the 12.5-GHz/44.45-Gbit/s IM/DD OFDM system with low-bandwidth (3.125 GHz) and sub-Nyquist sampling rate (6.25 GSa/s) ADC. The experiment results show that the proposed scheme can not only effectively achieve low-bandwidth reception, but also achieve about 0.4 dB receiver sensitivity improvement compared with the traditional high-bandwidth scheme at BER of 3.8×10-3 after 10.2 km standard single mode fiber transmission, which indicates that the proposed scheme is a promising low-cost candidate to provide large transmission capacity for the next-generation network.

A Low Complexity Sensing Algorithm for Non-Sparse Wideband Spectrum.

The vast majority of existing sub-Nyquist sampling wideband spectrum sensing (WSS) methods default to a sparse spectrum. However, research data suggests that in the near future, the wideband spectrum will no longer be sparse. This article proposes a sub-Nyquist sampling WSS algorithm that can adapt well to non-sparse spectrum scenarios. The algorithm continues to implement the idea of our previously proposed “no reconstruction (NoR) of spectrum” algorithm, thus having low computational complexity. The new one is actually an advanced version of the NoR algorithm, so it is called AdNoR. The key to its advancement lies in the establishment of a folded time-frequency (TF) spectrum model with the same special structure as in the fold spectrum model of the NoR algorithm. For this purpose, we have designed a comprehensive sampling technique which consists of multicoset sampling, digital fractional delay, and TF transform. It is verified by simulation that the AdNoR algorithm maintains a good sensing performance with low computational complexity in the non-sparse scenario.

Ghost edge detection based on HED network

In this paper, we present an edge detection scheme based on ghost imaging (GI) with a holistically-nested neural network. The so-called holistically-nested edge detection (HED) network is adopted to combine the fully convolutional neural network (CNN) with deep supervision to learn image edges effectively. Simulated data are used to train the HED network, and the unknown object’s edge information is reconstructed from the experimental data. The experiment results show that, when the compression ratio (CR) is 12.5%, this scheme can obtain a high-quality edge information with a sub-Nyquist sampling ratio and has a better performance than those using speckle-shifting GI (SSGI), compressed ghost edge imaging (CGEI) and subpixel-shifted GI (SPSGI). Indeed, the proposed scheme can have a good signal-to-noise ratio performance even if the sub-Nyquist sampling ratio is greater than 5.45%. Since the HED network is trained by numerical simulations before the experiment, this proposed method provides a promising way for achieving edge detection with small measurement times and low time cost.Graphical

Microwave Photonic Temperature Sensing Based on Fourier Domain Mode-Locked OEO and Temperature-to-Time Mapping

We report a novel temperature sensor based on a Fourier domain mode-locked optoelectronic oscillator (FDML OEO) and temperature-to-time mapping. In the proposed scheme, a narrow bandpass electrical filter is inserted into the FDML OEO cavity. The temperature information is mapped to the time interval of the output pulses due to the temperature-sensitive bidirectional scanning property of the FDML OEO. Compared with other OEO-based temperature sensors, the proposed scheme avoids the needs of wideband electrical spectrum analyzers, since the temperature-sensitive output pulses can be interrogated using a low-speed oscilloscope working under sub-Nyquist sampling condition. In the proof-of-concept experiment, a high sensitivity of 8.166 μs/°C and resolution of 0.03°C is achieved, demonstrating a good temperature sensing performance.

Joint frequency and DOA estimation of sub-Nyquist sampling multi-band sources with unfolded coprime arrays

Joint frequency and DOA estimation of sub-Nyquist sampling multi-band sources with unfolded coprime arrays

Computationally convolutional ghost imaging

The idea of using a single-pixel photodetector to sense the world may sound a little bit ambitious. However, a new type of computational imaging technology termed computational ghost imaging (CGI), is indeed making it a reality. No longer satisfied with using a non-spatially resolved photodetector to “see” the target, the computationally convolutional ghost imaging (CCGI) proposed in this paper can directly “see” the target’s features of interest without imaging first anymore. Rather than a conventional 4-f optical system, the CCGI scheme completes the convolution operations by optical methods with a single-pixel photodetector and an engineered structured illumination. Meanwhile, our CCGI scheme can adaptively work under sub-Nyquist sampling conditions, and it can facilitate real-time non-imaging edge detection of the real scene. With some multiplexing schemes, the prototype of CCGI has the potential as a new type of single-pixel computer vision that might be used as an optical frontend of a lightweight convolutional neural network to recognize objects intelligently. Our scheme brings new insights into both the convolution operation and the CGI technology, greatly broadening the application scenarios of CGI.

Compressive Wideband Spectrum Sensing and Signal Recovery With Unknown Multipath Channels

We study the problem of joint wideband spectrum sensing and recovery of multi-band signals in a multi-antenna-based sub-Nyquist sampling framework. Specifically, the multi-band signal is composed of a number of uncorrelated narrowband signals spreading over a wide frequency band. Unlike existing works which assume the source signals impinge on the receiver via a line-of-sight (LOS) path, we consider a more practical unknown MIMO channel which results from multipath propagation. A new sub-Nyquist sampling architecture is proposed, where each antenna output passes through two channels, namely, a direct path and a delayed path with a controlled amount of time delay. The signal at each channel is then sampled by a synchronized low-rate analog-to-digital converter (ADC). We utilize the collected data samples to build a set of cross-correlation matrices with different time lags and develop a CANDECOMP/PARAFAC (CP) decomposition-based method to recover the carrier frequencies, power spectra as well as the source signals themselves. Recovery conditions of the proposed method are analyzed, and Cramér-Rao bound (CRB) results for our estimation problem are derived. Simulation results are presented to illustrate the effectiveness of the proposed method.

Sequential-Based Range-Doppler Estimation With Fast and Slow Time Sub-Nyquist Sampling

Range-Doppler detection with pulse sequences exists widely in Radar, sonar, ultrasound imaging, and many other engineering applications. However, the classic methods require a high sampling rate for wideband pulses, and the Doppler estimation with slow time sub-Nyquist sampling may suffer from the phase wrapping. In this brief, a sequential-based range-Doppler estimation method with fast and slow time sub-Nyquist sampling is proposed. Utilizing the finite rate of innovation (FRI) theory, the range parameters can be estimated from several Fourier coefficients. The fast time sampling rate is determined by the number of the unknown parameters, instead of the signal bandwidth. Then, the aliasing-free Doppler parameters are estimated by the subspace method and the Chinese remainder theorem (CRT). The sequential-based method enables to estimate each Doppler parameter separately, and the Doppler estimation is transformed into a robust CRT problem, which enhances the robustness of the Doppler estimation. Simulation and hardware results demonstrate the effectiveness of the proposed method.

High-Frequency Ultrasound Imaging With Sub-Nyquist Sampling.

Implementation of a high-frequency ultrasound (HFUS) beamformer is computationally challenging because of its high sampling rate. This article introduces an efficient beamformer with sub-Nyquist sampling (or bandpass sampling) that is suitable for HFUS imaging. Our approach used channel radio frequency data sampled at bandpass sampling rate (i.e., 4/ 3fc ) and postfiltering-based interpolation to reduce the computational complexity. A polyphase structure for interpolation was used to further reduce the computational burden while maintaining an adequate delay resolution ( δ ). The performance of the proposed beamformer (i.e., 4/ 3fc sampling with sixfold interpolation, δ = 8fc ) was compared with that of the conventional method (i.e., 4fc sampling with fourfold interpolation, δ = 16fc ). Ultrafast coherent compounding imaging was used in simulation, in vitro and in vivo imaging experiments. Axial/lateral resolution and contrast-to-noise ratio (CNR) values were measured for quantitative evaluation. The number of transmit pulse cycles was varied from 1 to 3 using two transducers with different fractional bandwidths (67% and 98%). In the simulation, the proposed and conventional methods showed the similar -6-dB axial beam widths (63.5 and 61.5 μm , respectively) from the two-cycle transmit pulse using the transducer with a bandwidth of 67%. In vitro and in vivo imaging experiments were performed using a Verasonics ultrasound research platform equipped with a high-frequency array transducer (20-46 MHz). The in vitro imaging results using a wire target showed consistent results with the simulation study (i.e., disparity at -6-dB axial resolution). The in vivo feasibility study with a murine mouse model with breast cancer was also performed, and the proposed method yielded a similar image quality compared with the conventional method. From these studies, it was demonstrated that the proposed HFUS beamformer based on the bandpass sampling can substantially reduce the computational complexity while minimizing the loss of spatial resolution for HFUS imaging.

PUERT: Probabilistic Under-Sampling and Explicable Reconstruction Network for CS-MRI

Compressed Sensing MRI (CS-MRI) aims at reconstructing de-aliased images from sub-Nyquist sampling <i>k</i>-space data to accelerate MR Imaging, thus presenting two basic issues, <i>i.e.</i>, where to sample and how to reconstruct. To deal with both problems simultaneously, we propose a novel end-to-end Probabilistic Under-sampling and Explicable Reconstruction neTwork, dubbed PUERT, to jointly optimize the sampling pattern and the reconstruction network. Instead of learning a deterministic mask, the proposed sampling subnet explores an optimal probabilistic sub-sampling pattern, which describes independent Bernoulli random variables at each possible sampling point, thus retaining robustness and stochastics for a more reliable CS reconstruction. A dynamic gradient estimation strategy is further introduced to gradually approximate the binarization function in backward propagation, which efficiently preserves the gradient information and further improves the reconstruction quality. Moreover, in our reconstruction subnet, we adopt a model-based network design scheme with high efficiency and interpretability, which is shown to assist in further exploitation for the sampling subnet. Extensive experiments on two widely used MRI datasets demonstrate that our proposed PUERT not only achieves state-of-the-art results in terms of both quantitative metrics and visual quality but also yields a sub-sampling pattern and a reconstruction model that are both customized to training data.

Sub-Nyquist optical pulse sampling for photonic blind source separation.

We propose and experimentally demonstrate an optical pulse sampling method for photonic blind source separation. The photonic system processes and separates wideband signals based on the statistical information of the mixed signals, and thus the sampling frequency can be orders of magnitude lower than the bandwidth of the signals. The ultra-fast optical pulses collect samples of the signals at very low sampling rates, and each sample is short enough to maintain the statistical properties of the signals. The low sampling frequency reduces the workloads of the analog to digital conversion and digital signal processing systems. In the meantime, the short pulse sampling maintains the accuracy of the sampled signals, so the statistical properties of the under-sampled signals are the same as the statistical properties of the original signals. The linear power range measurement shows that the sampling system with ultra-narrow optical pulse achieves a 30dB power dynamic range.

Backtracking Reconstruction Network for Three-Dimensional Compressed Hyperspectral Imaging

Compressed sensing (CS) has been widely used in hyperspectral (HS) imaging to obtain hyperspectral data at a sub-Nyquist sampling rate, lifting the efficiency of data acquisition. Yet, reconstructing the acquired HS data via iterative algorithms is time consuming, which hinders the real-time application of compressed HS imaging. To alleviate this problem, this paper makes the first attempt to adopt convolutional neural networks (CNNs) to reconstruct three-dimensional compressed HS data by backtracking the entire imaging process, leading to a simple yet effective network, dubbed the backtracking reconstruction network (BTR-Net). Concretely, we leverage the divide-and-conquer method to divide the imaging process based on coded aperture tunable filter (CATF) spectral imager into steps, and build a subnetwork for each step to specialize in its reverse process. Consequently, BTR-Net introduces multiple built-in networks which performs spatial initialization, spatial enhancement, spectral initialization and spatial–spectral enhancement in an independent and sequential manner. Extensive experiments show that BTR-Net can reconstruct compressed HS data quickly and accurately, which outperforms leading iterative algorithms both quantitatively and visually, while having superior resistance to noise.

Sub-Nyquist Sampling of ECG Signals With Differentiated VPW Optimization Model

In recent years, developments in wearable technologies and wireless communication have enabled wearable ECG monitoring. Long-term ECG monitoring result in large amounts of data. To sub-Nyquist sampling ECG signal, recently developed finite rate of innovation (FRI) technology is a practical option. However, existing FRI sampling schemes generally suffered from large model mismatch errors and insufficient reconstruction accuracy. In this paper, a sub-Nyquist sampling scheme based on the differentiated VPW optimization model is proposed for ECG signals sampling. The original ECG signal is modeled as a linear combination of several differentiated Variable Pulse Width (VPW) pulses and a model mismatch error signal. Then, a two-channel sampling framework is proposed to sample ECG signals with a sub-Nyquist rate. To improve the accuracy of the reconstruction, optimizing the reconstruction is considered. We formulate the objective function of the optimization to minimize the model mismatch error signal. A particle filter-based optimization method is proposed to solve the objective function with a high-dimensional variable. Block coordinate descent (BCD) technique is considered in the proposed optimization method. Finally, we conduct several simulations with real ECG signals from MIT-BIH Arrhythmia Database to test the performance of our proposed scheme. Simulation results have demonstrated the reconstruction accuracy of our proposed scheme outperforms other related schemes.

Wideband spectrum sensing based on advanced sub-Nyquist sampling structure

As the bandwidth increases, the high-speed sampling rate becomes the bottleneck for the development of wideband spectrum sensing. Wideband spectrum sensing with sub-Nyquist sampling attracts more attention and modulated wideband converter (MWC) is an attractive sub-Nyquist sampling system. For the purpose of breaking the system structure limit, an advanced sub-Nyquist sampling framework is proposed to simplify the MWC system structure, adopting the single sampling channel structure with a frequency shifting module to acquire the sub-Nyquist sampling values. In order to recover the signal support information, the sensing matrix must be built according to the only one mixing function. Most existing support recovery methods rely on some prior knowledge about the spectrum sparsity, which is difficult to acquire in practical electromagnetic environment. To address this problem, we propose an adaptive residual energy detection algorithm (ARED), which bypasses the need for the above-mentioned prior knowledge. Simulation results show that, without requiring the aforementioned prior knowledge, the ARED algorithm based on the advanced sub-Nyquist sampling framework has the similar performance as MWC and even higher than MWC in some cases using only one sampling channel.

Progressive compressive sensing of large images with multiscale deep learning reconstruction

Compressive sensing (CS) is a sub-Nyquist sampling framework that has been employed to improve the performance of numerous imaging applications during the last 15 years. Yet, its application for large and high-resolution imaging remains challenging in terms of the computation and acquisition effort involved. Often, low-resolution imaging is sufficient for most of the considered tasks and only a fraction of cases demand high resolution, but the problem is that the user does not know in advance when high-resolution acquisition is required. To address this, we propose a multiscale progressive CS method for the high-resolution imaging. The progressive sampling refines the resolution of the image, while incorporating the already sampled low-resolution information, making the process highly efficient. Moreover, the multiscale property of the progressively sensed samples is capitalized for a fast, deep learning (DL) reconstruction, otherwise infeasible due to practical limitations of training on high-resolution images. The progressive CS and the multiscale reconstruction method are analyzed numerically and demonstrated experimentally with a single pixel camera imaging system. We demonstrate 4-megapixel size progressive compressive imaging with about half the overall number of samples, more than an order of magnitude faster reconstruction, and improved reconstruction quality compared to alternative conventional CS approaches.

Single pixel imaging via unsupervised deep compressive sensing with collaborative sparsity in discretized feature space.

Single-pixel imaging (SPI) enables the use of advanced detector technologies to provide a potentially low-cost solution for sensing beyond the visible spectrum and has received increasing attentions recently. However, when it comes to sub-Nyquist sampling, the spectrum truncation and spectrum discretization effects significantly challenge the traditional SPI pipeline due to the lack of sufficient sparsity. In this work, a deep compressive sensing (CS) framework is built to conduct image reconstructions in classical SPIs, where a novel compression network is proposed to enable collaborative sparsity in discretized feature space while remaining excellent coherence with the sensing basis as per CS conditions. To alleviate the underlying limitations in an end-to-end supervised training, for example, the network typically needs to be re-trained as the basis patterns, sampling ratios and so on. change, the network is trained in an unsupervised fashion with no sensing physics involved. Validation experiments are performed both numerically and physically by comparing with traditional and cutting-edge SPI reconstruction methods. Particularly, fluorescence imaging is pioneered to preliminarily examine the in vivo biodistributions. Results show that the proposed method maintains comparable image fidelity to a sCMOS camera even at a sampling ratio down to 4%, while remaining the advantages inherent in SPI. The proposed technique maintains the unsupervised and self-contained properties that highly facilitate the downstream applications in the field of compressive imaging.

Classification of the Ambiguity of Frequency Determination in a Digital Receiver with Multirate Sub-Nyquist Sampling

Classification of the Ambiguity of Frequency Determination in a Digital Receiver with Multirate Sub-Nyquist Sampling

High-Capacity Space-Division Multiplexing Communications With Silicon Photonic Blind Source Separation

Space-division multiplexing is a widely used technique to improve data-carrying capacities in both wireless and optical communication systems. However, tightly packed spatial channels cause severe crosstalk. High data rates and large channel counts impose severe constraints on resolving the crosstalk using traditional digital signal processing algorithms and electronic circuits. In order to solve these issues, this paper presents a silicon photonic system combining high-speed silicon photonic devices with a novel blind source separation (BSS) algorithm. We first demonstrate using photonic BSS to undo modal crosstalk in a short-reach multimode optical fiber interconnect for intra-data-center communications. The proposed photonic BSS system inherits the advantages of photonic matrix processor and the “blindness” of BSS, leading to superior energy and cost efficiency and reduced latency, while allowing to recover the signals using a sub-Nyquist sampling rate and in a free-running mode, and offering unmatched agility in signal format and data rate. The feasibility of using photonic processors for mode crosstalk equalization has been recently demonstrated, assisted with training sequences. Our approach, photonic BSS, in contrast, can tackle the more difficult problem of making the receiver transparent to any data rate and modulation format, and workable with slow and cost-effective electronics. In addition, we find that photonic BSS has a much better scaling law for space-division multiplexing (SDM)-based communication systems than digital signal processing (DSP). When compared to state-of-the-art DSP, photonic BSS can reduce system power consumption, speed, and latency by several orders of magnitude, particularly for high-capacity communications with high data rates per channel and a large number of channels. Photonic BSS has the added advantages of being agnostic to transmission content, making it exceptional at protecting communication privacy. This paper also discusses our previous work in demonstrating photonic BSS for privacy protection in wireless multiple-in multiple-out (MIMO) communications using silicon photonic micoring resonator (MRR) weight banks.

High-fidelity sub-Nyquist ghost imaging with tri-directional probing

Ghost imaging is an unconventional imaging method, which has invoked many applications in various fields. However, it is still a major challenge to achieve high-fidelity high-resolution images at a sub-Nyquist sampling rate. Here, we present a ghost imaging method that illuminates an object with three directional Tetris-like patterns, which can greatly trade off the contradiction between the high resolution and high detection signal-to-noise ratio. As the projected patterns gradually shrink during the detection, the image is also gradually recovered from low to high resolution. In addition, this method can recover complex chromatic objects without any compromising image quality by adaptively abandoning unnecessary patterns at sampling rates well below the Nyquist limit. Meanwhile, the dynamic probing scheme has an excellent noise-removal capability. The simulation and experiment demonstrate that the sampling rate to recover a high-fidelity image is only 10.7% for a scene of a 9.7% duty cycle. For a very noisy scene whose peak signal–noise rate (PSNR) is 10.18 dB [the structural similarity index (SSIM) is 0.068], this scheme increases the PSNR to 18.63 dB [structural similarity index (SSIM) to 0.73]. Therefore, the proposed method may be useful for ghost imaging in the low sampling rate regime or complex chromatic objects reconstruction.

A Modulated Wideband Converter Calibration Technique Based on a Single Measurement of a White Noise Signal with Advanced Resynchronization Preprocessing

The Modulated Wideband Converter (MWC) is a blind sub-Nyquist sampling system used especially to monitor wideband spectrum. This system can be realized by existing analog components. From a theoretical point of view, all analog components are assumed ideal. However, this hypothesis is false in practice. Indeed, some imperfections are introduced by analog components such as nonlinearities of mixers, phase/attenuation/selectivity of low-pass filters and desynchronization between modulating waveforms. Consequently, it is necessary to correctly estimate the sensing matrix to ensure correct spectrum reconstruction performance. Conventional calibration methods are based on the measurements of different single tones. However, these approaches need to record several measurements with single-tone inputs. To avoid this problem, this paper presents a new hardware calibration method of MWC by using a single measurement of a white noise signal for radio frequency spectrum monitoring. A preprocessing method is performed to resynchronize input, output and modulating waveforms signals with each other. Our hardware calibration method is applied to our prototype of Compressed Sensing (CS) scheme in order to estimate the corrected sensing matrix. To prove the efficiency of our hardware calibration, reconstruction performances were evaluated with respect to the probability of correct reconstruction and false alarm criteria. These results are compared with those obtained with the theoretical MWC scheme, with our prototype without calibration and with reference calibration.